论文标题
fell捆绑在准驻留订购的组和$ \ mathrm {c}^*$ - 紧凑型产品系统的代数
Fell bundles over quasi-lattice ordered groups and $\mathrm{C}^*$-algebras of compactly aligned product systems
论文作者
论文摘要
我们定义了在准命令订购组上的倒束的半饱和度和正交性的概念。我们表明，每当可简化时，都可以自然地扩展到半饱和且正交的掉束的希尔伯特双模模的产品系统。相反，半饱和且正交的跌倒束完全取决于阳性纤维及其横截面$ \ mathrm {c}^*$ - 代数对Hilbert Bimodules的简化产品系统的相对Cuntz--Pimsner代数是同构的。我们表明，这种对应关系是生物游戏之间的等效性的一部分，并在单个通信的背景下使用它来概括迈耶和作者的几个结果。我们将功能性应用于相对cuntz-pimsner代数来研究$ \ mathrm {c}^*$ - 连接到紧凑型产品系统上的$ \ mathrm {c}^*$ - 与Morita等效$ \ MATHRM {C}^*$ Algebras相比的代数。
We define notions of semi-saturatedness and orthogonality for a Fell bundle over a quasi-lattice ordered group. We show that a compactly aligned product system of Hilbert bimodules can be naturally extended to a semi-saturated and orthogonal Fell bundle whenever it is simplifiable. Conversely, a semi-saturated and orthogonal Fell bundle is completely determined by the positive fibres and its cross sectional $\mathrm{C}^*$-algebra is isomorphic to a relative Cuntz--Pimsner algebra of a simplifiable product system of Hilbert bimodules. We show that this correspondence is part of an equivalence between bicategories and use this to generalise several results of Meyer and the author in the context of single correspondences. We apply functoriality for relative Cuntz--Pimsner algebras to study Morita equivalence between $\mathrm{C}^*$-algebras attached to compactly aligned product systems over Morita equivalent $\mathrm{C}^*$-algebras.
